Antarctic Whale Project: Single Species
Ben Weinstein
2016-08-20 21:13:04
1 Descriptive Statistics
1.1 By Month
1.2 Distance
1.3 Time
1.4 Velocity
1.5 Angles
2 Correlated random walk
Process Model
\[ d_{t} \sim T*d_{t-1} + Normal(0,\Sigma)\] \[ x_t = x_{t-1} + d_{t} \]
2.1 Parameters
For each individual:
\[\theta = \text{Mean turning angle}\] \[\gamma = \text{Move persistence} \]
For both behaviors process variance is: \[ \sigma_{latitude} = 0.1\] \[ \sigma_{longitude} = 0.1\]
2.2 Behavioral States
\[ \text{For each individual i}\] \[ Behavior_1 = \text{traveling}\] \[ Behavior_2 = \text{foraging}\]
\[ \alpha_{i,1,1} = \text{Probability of remaining traveling when traveling}\] \[\alpha_{i,2,1} = \text{Probability of switching from Foraging to traveling}\]
\[\begin{matrix} \alpha_{i,1,1} & 1-\alpha_{i,1,1} \\ \alpha_{i,2,1} & 1-\alpha_{i,2,1} \\ \end{matrix} \]
2.3 Environment
Behavioral states are a function of local environmental conditions. The first environmental condition is ocean depth. I then build a function for preferential foraging in shallow waters.
It generally follows the form, conditional on behavior at t -1:
\[Behavior_t \sim Multinomial([\phi_{traveling},\phi_{foraging}])\]
With the probability of switching states:
\[logit(\phi_{traveling}) = \alpha_{Behavior_{t-1}} + \beta_{Month,1} * Ocean_{y[t,]} + \beta_{Month,2} * Coast_{y[t,]}\]
\[logit(\phi_{foraging}) = \alpha_{Behavior_{t-1}} \]
Following Bestley in preferring to describe the switch into feeding, but no estimating the resumption of traveling.
The effect of the environment is temporally variable such that
\[ \beta_{Month,2} \sim ~ Normal(\beta_{\mu},\beta_\tau)\]
2.4 Continious tracks
The transmitter will often go dark for 10 to 12 hours, due to weather, right in the middle of an otherwise good track. The model requires regular intervals to estimate the turning angles and temporal autocorrelation. As a track hits one of these walls, call it the end of a track, and begin a new track once the weather improves. We can remove any micro-tracks that are less than three days. Specify a duration, calculate the number of tracks and the number of removed points. Iteratively.
How did the filter change the extent of tracks?
## user system elapsed
## 198.285 1.609 10921.3442.5 Chains
2.5.1 Compare to priors
2.6 Parameter Summary
## Source: local data frame [38 x 5]
## Groups: parameter [?]
##
## parameter par mean lower upper
## (fctr) (fctr) (dbl) (dbl) (dbl)
## 1 alpha_mu alpha_mu[1] 0.01804063 -0.6497932 0.6681658
## 2 alpha_mu alpha_mu[2] -1.64435281 -2.2552399 -1.0862936
## 3 beta beta[1,1] -0.17076594 -1.8039178 1.9217257
## 4 beta beta[2,1] -1.52161389 -3.9871033 -0.1261102
## 5 beta beta[3,1] -1.52250167 -3.7409450 0.2167110
## 6 beta beta[4,1] -1.00901508 -2.5238436 0.5069955
## 7 beta beta[5,1] -0.56553751 -2.5615299 1.6717656
## 8 beta beta[9,1] -0.34906997 -1.8973933 2.0421645
## 9 beta beta[10,1] -1.23708135 -3.5817598 1.1308879
## 10 beta beta[1,2] 0.00000000 0.0000000 0.0000000
## .. ... ... ... ... ...
3 Behavior and environment
3.1 Hierarchical
3.1.1 Ocean Depth
3.1.2 Distance to Coast
3.2 By Month
3.2.1 Mean Estimates Only
3.2.2 As facets
3.2.3 Interaction
No estimate of uncertainty. 
4 Behavioral Prediction
4.0.1 Correlation in posterior switching and state
4.1 Spatial Prediction
4.1.1 Per Animal
## $`1`
##
## $`2`
##
## $`3`
##
## $`4`
##
## $`5`
##
## $`6`
##
## $`7`
##
## $`8`
##
## $`9`
##
## $`10`
##
## $`11`
##
## $`12`
##
## $`13`
##
## $`14`
##
## $`15`
##
## $`16`
4.2 Log Odds of Foraging
4.2.1 Ocean Depth
4.2.2 Distance From Coast
4.3 Autocorrelation in behavior
4.4 Behavioral description
4.5 Predicted behavior duration
Needs to be indexed by month.
4.6 Location of Behavior
5 Environmental Prediction - Probability of Foraging
5.1 Bathymetry
5.2 Distance to coast
5.3 All variables
## [[1]]
##
## [[2]]
6 Krill Fishery
## used (Mb) gc trigger (Mb) max used (Mb)
## Ncells 1773940 94.8 20145734 1075.9 39347138 2101.4
## Vcells 311452879 2376.2 1083541430 8266.8 1383093853 10552.2